Publication Date:
2020-11-10
Description:
This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function $k_{i}$ k i , namely, $$ egin{aligned} k_{i}^{prime }(t)le -xi _{i}(t) Psi _{i} igl(k_{i}(t) igr),quad i=1,2. end{aligned}$$ k i ′ ( t ) ≤ − ξ i ( t ) Ψ i ( k i ( t ) ) , i = 1 , 2 . We establish a new general decay result that improves most of the existing results in the literature related to this system. Our result allows for a wider class of relaxation functions, from which we can recover the exponential and polynomial rates when $k_{i}(s) = s^{p}$ k i ( s ) = s p and p covers the full admissible range $[1, 2)$ [ 1 , 2 ) .
Print ISSN:
1687-2762
Electronic ISSN:
1687-2770
Topics:
Mathematics
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